Twitter fact-checked President Donald Trump for the first time and, in response, Trump said he would end the social media platform. (The Minnesota Star Tribune)

President Donald Trump says a lot of things on Twitter that aren't true. Twitter has a set of formal policies designed to combat misleading information. This week, Twitter applied its policies to two of Trump's tweets, in which the president made misleading claims about voting by mail.

Trump responded with a threat:

"Republicans feel that Social Media Platforms totally silence conservatives voices. We will strongly regulate, or close them down, before we can ever allow this to happen."

The threat had an immediate effect on the stock of Twitter Inc.; it fell dramatically afterward.

To understand the controversy, we need to step back a bit. Social-media platforms such as Twitter, Facebook and YouTube are not subject to the Constitution at all. The First Amendment, which guarantees freedom of speech, applies only to the government. If Twitter denied a platform to Trump, or if it allowed only Republicans or only Democrats to have access to its platform, it would not be violating the Constitution.

Nonetheless, Twitter has good reason to allow something like a free-for-all. Its whole purpose is to permit plenty of diverse people to say plenty of diverse things. That's its business model. And if it's providing a public service, as I believe that it is, it should not favor any particular side. It should certainly not appoint itself as the truth police.

At the same time, the company has to draw some limits, and it does. Suppose that someone tweets that the presidential election will be held on Nov. 5 this year (it will actually be held on Nov. 3), or that people will not be allowed to vote unless they are at least 30 years old. Twitter does not allow that.

Or suppose someone says that "social distancing is not effective" to combat COVID-19, or that "walking outside is enough to disinfect you from the coronavirus." Twitter will not allow that either.

It doesn't try to remove every falsehood, but it also doesn't want its platform to be used to compromise public health. So in narrowly defined circumstances, it will remove material that it considers harmful.

This month, Twitter announced an updated approach to misinformation in general. Its basic approach consists of labels — warning people that what has been tweeted may not be true, and linking to sources that correct the record. If the potential harm is sufficiently severe, a tweet might be removed.

That is the background for the current controversy. In two tweets, Trump said that voting by mail is likely to create a significant increase in fraud. One said this:

"There is NO WAY (ZERO!) that Mail-In Ballots will be anything less than substantially fraudulent. Mail boxes will be robbed, ballots will be forged & even illegally printed out and fraudulently signed."

Twitter appended a short label, saying, "Get the facts about mail-in ballots." As a spokesperson for Twitter explained, the president's tweets "contain potentially misleading information about voting processes and have been labeled to provide additional context around mail-in ballots."

It should be clear that Twitter's approach was fully in line with its current policies and also that it was quite mild. Twitter did not remove Trump's tweet. It did not say that it was false. Indeed, it did not even declare that it was misleading. It said publicly that it was only "potentially misleading." Its small label informed people how to "get the facts."

It is perfectly acceptable for a newspaper or magazine to correct the record about public officials — to say, for example, that President Bill Clinton misled the public about his relationship with Monica Lewinsky.

But social-media platforms are not newspapers or magazines, and they have to strike a difficult balance. They cannot be expected, and should not be asked, to take down every falsehood that appears on their platforms. But it is legitimate for them to adopt neutral policies that are designed to educate and inform users about misinformation, or about potentially misleading material.

There is an irony here. Trump rightly emphasizes the value of freedom of speech, and even though Twitter is unconstrained by the First Amendment, he is correct to say that the company should respect that value. At the same time, a central purpose free speech is to ensure an informed public. With respect to misleading tweets, Twitter's policy promotes that value — which means that it should be praised, not threatened.

Cass R. Sunstein is the author of "The Cost-Benefit Revolution" and a co-author of "Nudge: Improving Decisions About Health, Wealth and Happiness."